Instructor Introduction

Three Major Course Components

• Lectures on foundational material
  • Slides posted online
  • Lectures recorded and linked on Piazza
• Paper presentations by students followed by discussion
  • Non-presenters required to submit a brief (2-3 sentence) summary and discussion question
  • Piazza participation for asychronous students
• Project
  • To be done alone or in teams of up to 3
  • Papers can provide inspiration; project could be an implementation or extension of one of these, or application of existing implementations to a new domain
  • Complexity of project may be adjusted to student level

Geometry - γεωμετρία

geo = earth

Geometry - γεωμετρία

geo = earth

Geometry - γεωμετρία

metria = measure

A little bit of History

Images from Wikipedia

A little bit of History

Classic Geometry was based on compass-and-straightedge construction

Images from Wikipedia

A little bit of History

Images from Wikipedia

A little bit of History

• Modern Geometry joins classic geometry and algebra/calculus
• Analytic Geometry = Geometry with coordinates and equations
• Add in ability to compute, and Geometry Processing results
• “science of shape”:
  • length
  • area
  • volume
  • angle
  • curvature
  • deformation
  • …

A little bit of History

Our goal is complex geometry for simulation and animation

3D Scanning

Cultural Heritage

© Digital Michelangelo Project

Urban Modeling

Automotive Industry

Digital Avatars

© ICT

Computational Fabrication

Course Content

Course Content

Course Content

Course Content

Course Content

Detailed Course Information

• Attending class
  • Lecture: 11:00 AM - 12:15 PM, Tuesdays and Thursdays, MCS B31, Zoom link
  • In-person attendance scheduled via InClassLfA app; done biweekly with deadline at Thurs. 1 PM
  • I will ask that videos be on, to encourage participation
  • Lectures and discussions will be recorded; doesn’t apply to breakout rooms
  • Please bring materials for virtual participation, even if you participate in person
• Office hours
  • Virtual, 12:30 - 1:30 PM, Tuesdays and Thursdays Zoom link

Detailed Course Information

• Piazza will serve as the main resource center for the course
  • Main hub for discussion
  • Course syllabus, tentative schedule, growing paper list already up
  • Links to recordings
• Slides to be posted online, on my website
• Gradescope for turning in assignments
  • Paper summaries
  • Project progress reports

Paper Readings & Discussion

• 20 minutes for student presentation of the paper in question
• 20 minutes for discussion in breakout groups
• 20 minutes for discussion as a class (or I may give some context or a brief overview of relevant methods)
• Non-presenters required to submit a brief (2-3 sentence) summary and discussion question
• Piazza participation for asychronous students

Project

• To be done alone or in teams of up to 3
• Papers can provide inspiration; project could be an implementation or extension of one of these, or application of existing implementations to a new domain
• Small weekly progress reports will need to be turned in
• Final project presentation to be done at the end
• Complexity of project may be adjusted to student level

Tentative Schedule

See doc

Recommended Prerequisites

• Working knowledge of programming and data structures (CAS CS 111 and CS 112, or equivalent). The most useful languages/platforms are C++ and Matlab, but you can use any language you like for your final project.
• A strong foundation in linear algebra (CAS CS 132 or MA 242 or equivalent).
• A strong foundation in multivariable calculus (MA 225 or equivalent)
• Additional background in differential geometry or topology could be quite helpful, but is not necessary, as projects may be tailored towards students’ level of knowledge.
• Project may be tailored to you’re level of preparation. If you’re unsure, feel free to talk to me.

How to use our HTML slides

• Use the keys left/right to navigate through the slides.
• Click page number (bottom right) to open navigation menu.
• Press f/ESC to enter/leave fullscreen mode
• Double-click an item (e.g. an image) to zoom in/out.
• If the whiteboard icon is highlighted red () something was written to the virtual whiteboard. Click the icon to show/hide the whiteboard.
• Use Chrome/Chromium or Firefox 👍. Do not use Safari, it cannot handle WebGL demos 👎.

Slide Acknowledgements

Other resources (even courses!)

• Polygon Mesh Processing by Kobbelt et al.
• Numerical Algorithms: Methods for Computer Vision, Machine Learning and Graphics by Justin Solomon
• Libigl - a header-only C++ geometry processing library: https://libigl.github.io/
• Open Flipper - another C++ geometry processing platform: https://www.graphics.rwth-aachen.de/software/openflipper/
• David Bommes’s course @ Uni Bern
• Justin Solomon’s course @ MIT
• Keenan Crane’s course @ CMU
• Alec Jacobson’s course @ UToronto